Problem: Which of the following numbers is a multiple of 6? ${43,55,84,89,119}$
Explanation: The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $43 \div 6 = 7\text{ R }1$ $55 \div 6 = 9\text{ R }1$ $84 \div 6 = 14$ $89 \div 6 = 14\text{ R }5$ $119 \div 6 = 19\text{ R }5$ The only answer choice that leaves no remainder after the division is $84$ $ 14$ $6$ $84$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $84$ $84 = 2\times2\times3\times7 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $84$. We can say that $84$ is divisible by $6$.